The following is a copy of RRAA postings by Roy Lewallen
W7EL about inductors. I think
the technical portion of these posts are useful for understanding current in
loading coils, and how we need to cross check theories properly. I've included all of the text,
even though much text is not technical. This really is educational, so read it
if you have time!!!

I think the goal should be education, not conversation,
so I enlarged important text size and changed color to blue in what I think are important areas.

Comments of mine are in RED.

W8JI Tom

The following are verbatim copies of postings made on
rec.radio.amateur.antenna, in the thread "Re: Current in antenna loading coils controversy" (first posting), "Re: Current in antenna loading coils controversy - new measurement" (last posting), and "Re: Current in antenna loading coils controversy (long)" (remainder of postings). I and others made many additional postings on the topic, which should be available at
http://www.groups.google.com.

Roy Lewallen
January 11, 2004
Posted on 11-4-03:
No, I will make one more comment. After a bit of reflection, I think this might be at the core of some people's problem in envisioning a lumped inductor.When a current flows into an inductor, it doesn't go round and round and round the turns, taking its time to get to the other end. An inductor wound with 100 feet of wire behaves nothing like a 100 foot wire. Why? It's because when the current begins flowing, it creates a magnetic field. This field couples to, or links with, the other turns. The portion of the field from one turn that links with the others is the measurable quantity called the coefficient of coupling. For a good HF
toroid, it's commonly 99% or better; solenoids are lower, and vary with aspect ratio. The field from the input turn creates a voltage all along the wire in the other turns which, in turn, produce an output current (presuming there's a load to sustain current flow). Consequently, the current at the input appears nearly instantaneously at the output. Those who are physics oriented can have lots of fun, I'm sure, debating just how long it takes. The field travels at near the speed of light, but the ability of the current to change rapidly is limited by other factors.

So please flush your minds of the image of current whirling around the coil, turn by turn, wending its way from one end to the other. It doesn't work at all like that. The coupling of fields from turn to turn or region to region is what brings about the property of inductance in the first place.

That was a great explanation of how an
inductor works. I often learn new or better ways to view things when reading
what Roy writes!

Radiation is another issue, and provides a path for current, via displacement current, to free space. (I can see it now in Weekly World News: WORLD FILLING WITH COULOMBS! DISASTER LOOMS!) For a component to fit the lumped element model, radiation has to be negligible. And, for the same reason, it can't be allowed to interact with external fields as a receiver, either.

This is very fundamental stuff. You can find a lot more about the topic in any elementary circuit analysis or physics text. If you don't believe what you read there, just killfile my postings -- you won't believe me, either, and reading what I post will be a waste of time for both of us.

Real inductors, of course, are neither zero length nor do they have a perfect coefficient of coupling. And they do radiate. The essence of engineering is to understand the principles well enough to realize which imperfections are important enough to affect the outcome in a particular situation. We simplify the problem by putting aside the inconsequential effects, but don't oversimplify by ignoring factors that are important for the job at hand. Those who insist on using only the simplest model for all applications will often get invalid results. And those who use only the most complex model for all applications (as is often done in computer circuit modeling), often lose track of what's really going on -- they become good analysts but poor designers. I've seen people capable of only those approaches struggle, and fail, to become competent design engineers.

And with that, I'm outta here. Hope my postings have been helpful.

Posted 11-8-03:
Here are some preliminary details about the inductor current measurement I made.

My antenna isn't nearly as ideal as the one Yuri described. (But if my results are different from the ones reported at the web site Yuri referenced, I'll be eager to hear why.) It's about 33 feet high, and has only 7 buried radials. The feedpoint impedance indicates a loss of about 25 ohms at 7 MHz, so I'd expect it to be a bit more at 3.8. It's bolted to a galvanized fence line post which protrudes nearly four feet from the ground, with spacing between the antenna and the post of about 1/4". This mounting has only a minor effect on the feedpoint impedance at 7 MHz, which is the antenna's intended frequency of use. It's quite profound at 3.8 MHz, though. The expected 370 or so ohms of capacitive reactance is transformed to 185, while the feedpoint R is 35 ohms, not far from the expected value. So the overall feedpoint Z is 35 - j185 ohms at 3.8 MHz, measured with a GR 1606A impedance meter. (I found that my MFJ 269 was about right with the X, but measured R as zero -- apparently the combination of low frequency and large X is a problem for it in resolving the R.) So I built an inductor with measured impedance of 0.6 + j193 ohms. It's 26 turns on a T-106-6 toroid core. Q is a bit over 300. This was placed in series at the antenna feedpoint.

For current measurements, I made two identical current probes. Each one consists of 10 turns wound on an FT-37-73B ferrite core. The two leads from the winding are twisted and wound in bifilar fashion on another FT-37-73B core, 10 turns. This is then connected to an oscilloscope input via a two-foot (approx.) piece of RG-58. A 50 ohm termination is also at the scope input. This gives the probe a theoretical insertion impedance of 0.5 ohm. While making the measurements, I moved, grabbed, and re-oriented the coax cables, with no noticeable effect. This gave me confidence that the outsides of the coax weren't carrying any significant current.

One probe went to each channel of the scope. I left the two scope inputs in the cal position, put both probes on the wire at the input end of the inductor, and recorded the p-p values with the scope's digital measurement feature. Then I reversed the order of the probes and
remeasured. I found a slight prejudice toward the probe closest to the source -- 1.2% in one ordering, and 2.1% in the other. Averaging the two channels, though, showed them to be the same within less than 1%. (Each probe was always connected to the same scope channel, so this is a test of the probe-scope channel combinations.)

Then I moved one probe to the output side of the inductor, and measured input and output current. And I reversed the probe positions on inductor input and output. The ratio of output to input current in the two tests differed by only 1.4%.

When I encounter an astrologist, they invariably ask what "sign" I "am", then proceed to tell me how my personality meets their expectations. So what I do instead is to have them tell *me* what "sign" I "am" *first* -- which they should easily be able to do, based on my personality. Well, they don't find that to be fair, for some reason (although I certainly find it amusing). And so, I doubt if the following challenge will be regarded to be fair, for much the same reason. Those with alternative rules for solving circuit problems are challenged to predict what the ratio of output current to input current will be. I'm particularly targeting Cecil, and others who have bandied about a lot of pseudo-analysis about electrical length, reflections, and the like. And, Richard (Harrison), who said something like "an inductor without phase shift is like". . . I don't recall. . .hot dog without ketchup or something. Pull out your theories, and calculate it, like any competent engineer should be able to do. For
cryin' out loud, it's a simple series circuit (except for Cecil, where it's some kind of distributed thing).

First post your answers, then I'll post the result of my measurements.
Roy Lewallen, W7EL

Posted on 11-11-03:
It sounds like the predictions are in. Among the several people who believe that the current out of a small inductor doesn't equal the current in, only Yuri was able to calculate a predicted value for the test, of 2.5 - 5% reduction in current at the output compared to the input, with a phase shift of about 18 degrees.

You see above Yuri "predicted" a
current value based on a cosign formula that relates to antenna area. One way to
test a theory is to change the conditions or parameters of the test, and see if
the predictions apply in multiple cases or if it was just a "guess" or
dumb-luck. This is ALWAYS a good idea. Watch what happened when Roy changed the
antenna length and used the same formula!

What I measured was a 3.1% reduction in magnitude from input to output, with no discernible phase shift. The 3.1% is an average of two readings, with the input and output probes exchanged. The output was smaller than the input in both measurements, about 2% and 4%. So I believe there's a real difference between output and input current, although with the accuracy of my measurements, I only have reasonable confidence it's somewhere between 1 and 5%. I can resolve about 2-3 degrees of phase shift, though, and I couldn't discern any at all. (Yes, the scope trigger was from one channel, not alternating.) So I have very high confidence that Yuri's prediction of 18 degrees is
incorrect.

I don't subscribe to the notion that the current out of a very small inductor should be different than the current in due to some magical property it acquires when connected to an antenna. My working hypothesis is that the current difference I did see was due to stray capacitance, either from the probes or simply to the Earth and other objects. It would take an equivalent of 6.8 pF at the output of the coil (that is, between the coil output and the current probe) to get 3% reduction, and only about 1/3 that amount to see the minimum value of reduction of 1% I estimate was actually present.

Here is where Roy changed the test. Now the
coil isn't in an antenna, and the "sine rule formula" should not
apply. If the sine rule was correct, the current differential should have
changed significantly.

I repeated the test on the bench, with a 36 ohm resistor in series with a 220 pF capacitor substituting for the antenna. The result was a 2.3% output:input reduction, again with no discernible phase shift. This is
within the measurement error of being the same result. This is what should be expected -- except for unintentional coupling to the antenna's field, the inductor's environment is the same on the bench as at the antenna base, in these single frequency, steady state tests. (That also contradicts what some newsgroup participants have been claiming.)

So, although the small output:input current reduction was within Yuri's prediction, the phase shift certainly wasn't. If time permits, I'll make a more idealized antenna and repeat the measurements with a larger inductor at the base of a more reactive antenna. I'll predict in advance that if I double the amount of loading L, I'll approximately double the amount of current magnitude attenuation -- that is, to somewhere around 6%. That's what should be expected if the cause of the attenuation is stray C or a similar phenomenon.

Posted on 11-11-03:
Today's project was to construct and measure a more idealized antenna.

The antenna is 33 feet high, made of #16 insulated wire. I put out 23 radials on the surface of the wet ground. Radials were of various lengths, most about 30 feet long. The feedpoint impedance of the antenna, measured with a GR bridge, was 15.8 - j437 ohms at 3.8 MHz. Allowing 3% lengthening effect for insulation, EZNEC says a lossless vertical of that height and diameter should have an input Z of 7.5 - j478. 8.3 ohms loss resistance is reasonable for that number of radials, and the somewhat lower than predicted reactance is likely due to the fact that the radial wires were grouped together as they came up a few inches to the antenna base, and not immediately coming in contact with the ground. That would add a bit of inductive reactance.

I wound an inductor on a T-106-6 core as before, but with more turns, for a measured Z of 1.3 + j387 ohms. After putting it in series with the antenna at the base, the base impedance measured 17.1 - j54 ohms. This is only 4 ohms from the expected reactance, and spot on the expected resistance, so measurements are consistent.

Analyzing verticals with EZNEC, made from #16 wire at 3.8 MHz, shows that:

-- An antenna 63.2' high is resonant.
-- An antenna 35.9' high has a feedpoint reactance of -j437 ohms.
-- An antenna 59.35' high has a feepoint reactance of -j54 ohms.

With a resonant height of 63.2', you could say that 63.2' is "90 electrical degrees" as far as the antenna is concerned. So you might say that my inductor has "replaced 33.4 electrical degrees" of the antenna.

Here again the test is modified to test Yuri's
prediction.

Using Yuri's cosine rule, we should then expect the inductor output current to be cos(33.4 deg) times the input current, or 16.5% less. Also, we should expect to see those 33 degrees of "replaced antenna" as phase shift from the input to the output of the inductor. That is, the current change from the input to output of the inductor is the same as it would be for the portion of the antenna it "replaces". (I think Jim Kelley subscribes to this theory also, but I'm not sure.)

In contrast, conventional electrical circuit theory predicts no current difference between the input and output for a physically very small inductor with no radiation or stray coupling. I saw about 3% in the previous measurement, which I believe can be attributed to stray capacitance. So I predicted that we should see about twice that amount with the higher valued inductor used for this experiment (387 vs 192 ohms reactance). I didn't see any measurable phase shift between input and output before, so I didn't expect to see it this time.
So for this test, there's quite a difference in predictions for output:input current --**Yuri's method predicts a reduction of output current magnitude of 16.5% and a phase shift of 33 degrees.

I have very high confidence that my measurements are good enough to resolve the difference between these two possibilities.
Would anyone care to comment before I post the measurement results? And, Yuri, please correct me if I've misinterpreted your theory.
Roy Lewallen, W7EL

Here are the test results, still using the
same formula. If the results of the Cos theory and formula are correct, the
results would be 16.5% current reduction and 33 degrees phase shift. This shows
why it is important to test new formulas in a variety of
applications.

Posted on 11-11-03:
Ok,For anyone who cares, the magnitude of the current out of the inductor in the later test measured 5.4% less than the current in. No phase shift was discernible. An analytical person could build on this information to investigate the properties of longer inductors placed elsewhere in the antenna.
Thank you for the comments, Cecil, Yuri, Richards, Art, and others. I've learned a good lesson from this -- that this isn't an appropriate forum or appropriate audience for the sort of quantitative analysis and reasoning I'm familiar and comfortable with. And that the considerable time and effort required to make careful measurements is really of very little benefit -- certainly not anywhere near enough to justify it.
With a great sigh of relief from everyone, I'm sure, I'll now turn this thread back over to Yuri, Cecil, et al.
My apologies to everyone for taking up so much bandwidth.
73,
Roy Lewallen, W7EL

So there we have it. The Cosine theory that
states an inductor replaces part of the antenna and has the same or similar
phase shift and current taper as that part of the antenna proved false once the
system was perturbed. It is quite typical for a formula that is incorrect to
work at one point just by sheer luck.

When we have a theory, the test is to apply
that theory to various systems and see if it works in all cases. If it does not
work in all cases, the theory is incorrect.

While I agree it should not be necessary to
prove conventional circuit theory, I think Roy's test (and my test) might shed
some useful insight into how short and heavily loaded antennas actually work. A
secondary benefit is we see how an incorrect idea or concept can actually work
once in a while just by sheer luck, and why we need peer review.

Many people have the misplaced notion a wire
in an inductor replaces a certain "electrical length" of the antenna.
That isn't true. A loading inductor simply cancels reactance (corrects power
factor). Current change across the inductor actually indicates a problem with
the inductor, unless it is intentional.